I will take a shot at it.

The best way for me to see this is to try it on a very simplified
contest flight.

So let’s try a 1 hour task. With a Start Gate at a maximum of 7000
feet and the finish gate at a minimum of 1000 feet. Lift is a
constant 250 ft/min.

Of course you will want to start as high as possible which will be
7000 feet.

I am going to use a hypothetical glider to keep the number simple.
Lets say your best speed is 60 MPH at a 250 ft/min descent.

#1 So from your start i.e. your 1st thermal you can lose 6000 feet to
put you at 1000 feet AGL. At 250ft/min this will take 24 minutes and
you will glide 24 miles. At this point you pick up another 250 ft/min
thermal and climb to 5500 ft. this takes another 18 minutes so you
have a total of 42 minutes on course. You then glide for 18 minutes
back to the finish line taking another 18 minutes to finish right at
1000 feet. So you have been on course for exactly 1 hour and have
covered 42 miles.
Your speed is 42 miles per hour.

#2 so, the same day but you decide to stay on course a bit longer. So,
on the 2nd thermal instead of climbing to 5500 feet you climb to 7000
feet. And fly some extra distance with extra the altitude. So it takes
you 24 minutes to climb to 7000 feet and you glide 24 miles to the
finish. This gives you a time on course of 72 minutes and distance of
48 miles for a speed of 48/1.2 = 40 MPH.

#3 let’s say you decide to take another thermal from the last example.
So at the 72 minute mark you hit another thermal and climb to 7000
feet this adds another 24 minutes, but of course you can glide for
another 24 minutes. So this gives you a time on course of 72+24+24 =
120 minutes and a distance of 72 miles. So your speed is 72 / 2 = 36
mph.

The reasoning that the speed gets slow the longer you stay out is that
you were given the 1st thermal. Try calculating this as if the maximum
start gate was 1000 feet.

#1 you climb to 7000 feet taking 24 minutes. You glide for 24
minutes. You climb for 6 minutes and glide for 6 minutes to the
finish. You are still 1 hr and have flown 30 miles for 30 MPH
average.

#2 you climb to 7000 feet taking 24 minutes, you glide for 24 minutes
you climb for 12 minutes and glide for 12 minutes. You time is 72
minutes and your distance is 36 miles.
Your speed is 36 / 1.2 = 30 MPH.

#3 You climb to 7000 feet and glide 24 miles for 48 minutes you climb
again to 7000 feet and glide another 24 minutes. As you can see it is
taking you 48 minutes for 24 miles. So a third thermal will take
another 48 minutes so you total time on course is 48* 3 Thermals = 144
minutes. Your distance is 24*3 = 72 miles. So your Speed is 72 / 2.4
hrs = 30 MPH.

So this demonstrates that since we start at the top of the 1st thermal
under consistent conditions it is advantages to come in as close to
the minimum time as you can.

Your course in reality changing conditions can change what is the best
strategy; however I hope this answers your question.

Brian